Math @ Duke

Publications [#246923] of JianGuo Liu
Papers Published
 Chen, GQ; Liu, JG, Convergence of difference schemes with high resolution for conservation laws,
Mathematics of Computation, vol. 66 no. 219
(1997),
pp. 10271053
(last updated on 2017/12/18)
Abstract: We are concerned with the convergence of LaxWeridroff type schemes with high resolution to the entropy solutions fo: conservation laws. These schemes include the original LaxWendroff scheme proposed by Lax and Wendroff in 1960 and its two step versionsthe Richtrayer scheme and the MacCormack scheme. For the convex scalar conservation laws with algebraic growth flux functions, we prove the convergence of these schemes to the weak solutions satisfying appropriate entropy inequalities. The proof is based on detailed Lp estimates of the approximate solutions, H1 compactness estimates of the corresponding entropy dissipation measures, and some compensated compactness frameworks. Then these techniques are generalized to study the convergence problem for the nonconvex scalar case and the hyperbolic systems of conservation laws.


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